Research Areas

My research is  focused on the analysis of the nonlinear PDEs with the primary focus on  equations arise in fluid dynamics and wave theory. I am mainly interested in the existence, uniqueness and regularity of the PDEs arise in this field.   I also address some quantitative properties of solutions to these kind of equations, namely: long time behavior as well as stability.   In my research, I apply a wide range of advanced techniques in harmonic analysis and PDE's, including Littlewood--Paley theory.  In addition, I make use of the methods in dynamical systems, and my recent works on both decay rates and stability of PDE's rely heavily on the spectral theory.

 In this context, I have worked on the Navier-Stokes systems and wave theory. Since their derivation, many physical phenomena are modeled by wave equations and  Navier-Stokes systems. Navier-stokes systems are usually derived by coupling the Navier-Stokes equations with other equations. For example the Magnetohydrodynamics (MHD) system consists of a coupling of the Navier-Stokes equation with the Maxwell's equation, and models the magnetic properties of electrically conducting fluids, including plasma, liquid metals, electrolytes, etc. 

Projects in preparation


Publications